Answer
Domain: $(-\infty,\infty)$
Range: $(2,\infty)$
Asymptote: $y=2$
Work Step by Step
We are given the function:
$$g(x)=2+e^x.$$
Consider the function $f(x)=e^x$ as the parent function. We obtain the graph of $g$ by vertically shifting the graph of $f$ by $2$ units (see the graph).
From the graph we determine the following elements of function $g$:
- the domain:
$$\text{domain}=(-\infty,\infty)$$
- the range:
$$\text{range}=(2,\infty)$$
- the horizontal asymptote:
$$y=2.$$